(a) By branching on x 2 , use the branch-and-bound method to solve the following integer programming...
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(a) By branching on x 2 , use the branch-and-bound method to solve the following integer programming problem (IP):
Maximize z 6x 1 + 2x 2
Subject to
5x 1 + x 2 ≤ 10
2x 1 +x 2 ≤ 9
x 1 . x 2 ≥ 2 0; x 1 , x 2 integer.
b) A hiker has a 5-ft backpack and needs to decide on the most valuable items to take on the hiking trip. There are three items from which to choose. Their volumes are 2, 3, and 4 ft 3, and the hiker estimates their associated values on a scale from 0 to 100 as 30, 50, and 70, respectively. Formulate the problem as an LP model and what kind of linear programming is it?
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